For the function y=4-2x^2+1/6x^4 find the following:

Question

Domain
x and y intercepts
Vertical asymptotes
Horizontal asymptotes
Symmetry
F'(x)
Critical numbers
Increasing f(x)
Decreasing f(x)
Extrema
F"(x)
Possible points of inflection
Concave up
Concave down
Points of inflection

I got some:
domain: (-infinity, infinity)
y-intercept: y=4
Symmetry: y-axis
F'(x): 2/3x^3-4x
Critical numbers: x=0, x=sqrt6, x=-sqrt6
F"(x): 2x^2-4
Possible points of inflection: (sqrt2, 2/3) (-sqrt2, 2/3)
Concave up: (-infinity, -sqrt2) and (sqrt2, infinity)
Concave down: (-sqrt2, sqrt2)

Answer 1

I figured out some more I think
Vertical asymptotes: none
Horizontal asymptotes: none
Extrema: relative maximum f(0)=4, relative minimums f(-sqrt2)=-2 and f(sqrt2)=-2

Would I need absolute extrema? There aren't any end points.